Theoretically hashing something 2^128 times with the MD5 algrithm [closed]

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This is a purely hypothetical question, but if you were to start with 128 bits, and then hash them 2^128 times, say with the MD5 algorithm, would you eventually come back to your original bits? Would all possible combinations have been used? And if not, are there certain nubers that "hash back to themselves" faster than others?

I assume this is practically impossible to achieve (after looking at my calculators answer to 2^128...), and I'm pretty sure the answer would be different for different algorithms, but that doesn't stop one from theoretizing, does it?

So yeah, that's it, hope someone out there will have some more knowledge on this topic. Looking forward to seeing the answer(s), thanks in advance!

Edit: To clarify: What interests me the most in this question is if it will go through all possible bit combinations or if there rather are several smaller cycles, tho any additional, relevant and interesting information is appreciated.

Answer 1

A good cryptographic hash should have some, but not too many, cycles in it, that makes it much harder to create rainbow tables for it. This occurs in the MD5 - actually a problem with MD5 is that it's a bit to easy too find hash collisions for a given hash for the algorithm. This weakness makes it computationally feasible to inject malicious data in a file that is hashed with MD5 for verification.

I think you think there's some Fermat's little theorem property of the MD5, but this is not the case. The hash function will probably start to walk in circles quite soon, and it should.

There's also a very memory efficient way to find MD5 cycles. Also have a look at MD5CRK.

If you really want a unique "hashing" of an 128-bit id, you should use an ordinary encryption algorithm, for instance with AES, of a particular number and a secret key. This gives you a "random", unique row of numbers form an increasing id, since you can always decrypt the information in a unique way, given the same key that was used to encrypt the data.